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Issue 13, 2019
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Revising the measurement process in the variational quantum eigensolver: is it possible to reduce the number of separately measured operators?

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Abstract

Current implementations of the Variational Quantum Eigensolver (VQE) technique for solving the electronic structure problem involve splitting the system qubit Hamiltonian into parts whose elements commute within their single qubit subspaces. The number of such parts rapidly grows with the size of the molecule. This increases the computational cost and can increase uncertainty in the measurement of the energy expectation value because elements from different parts need to be measured independently. To address this problem we introduce a more efficient partitioning of the qubit Hamiltonian using fewer parts that need to be measured separately. The new partitioning scheme is based on two ideas: (1) grouping terms into parts whose eigenstates have a single-qubit product structure, and (2) devising multi-qubit unitary transformations for the Hamiltonian or its parts to produce less entangled operators. The first condition allows the new parts to be measured in the number of involved qubit consequential one-particle measurements. Advantages of the new partitioning scheme resulting in severalfold reduction of separately measured terms are illustrated with regard to the H2 and LiH problems.

Graphical abstract: Revising the measurement process in the variational quantum eigensolver: is it possible to reduce the number of separately measured operators?

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Supplementary files

Article information


Submitted
14 Dec 2018
Accepted
11 Feb 2019
First published
12 Feb 2019

This article is Open Access
All publication charges for this article have been paid for by the Royal Society of Chemistry

Chem. Sci., 2019,10, 3746-3755
Article type
Edge Article

Revising the measurement process in the variational quantum eigensolver: is it possible to reduce the number of separately measured operators?

A. F. Izmaylov, T. Yen and I. G. Ryabinkin, Chem. Sci., 2019, 10, 3746
DOI: 10.1039/C8SC05592K

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